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DRDO Multi tasking staff Model paper 5

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Question : 88 of 100

Marks: +1, -0

Find the sum of the series:

\frac{3}{4}+\frac{5}{36}+\frac{7}{144}+\frac{9}{400}+\frac{11}{900}

48/49
35/36
5/6
143/144

Solution:

\frac{3}{4}+\frac{5}{36}+\frac{7}{144}+\frac{9}{400}+\frac{11}{900}

In such series, try to make 2 factors of denominator such that their difference is equal to numerator.

⇒

\frac{3}{1\times 4}+\frac{5}{4\times 9}+\frac{7}{9\times 16}+\frac{11}{25\times 36}

⇒

\frac{3}{1^2\times 2^2}+\frac{5}{2^2\times 3^2}+\frac{7}{3^2\times 4^2}+\frac{9}{4^2\times 5^2}+\frac{11}{5^2\times 6^2}

⇒

\frac{(3+5+7+9+11)}{1^2\times 6^2}

⇒35/36

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